From the experiments and results shown in the previous sections, we can see that, by formulating quantum ansätz search as a tree-based search problem, one can easily impose various kinds of restrictions (`hard limits') on the circuit structure, leading to the pruning of the search tree and the search space. Also, by introducing Placeholders, one can explore smaller circuit sizes. Since current deep reinforcement learning algorithms struggle when the state space is large but the number of reward states is small. Compared to other research work in quantum ansätz search, including the differentiable quantum ansätz algorithm proposed in [1]}, and other QAS algorithms based on meta-learning [2]} or reinforcement learning [3]}, which only investigate small-scale problems, like 3- or 4-qubit quantum Fourier transform in [1]}, 3-qubit classification task and 4-qubit \(\text{H}_2\)  ground state energy problem in [5]}. A larger example can be seen in [6]}, which is a 6-qubit transversal Ising field model. In our research, we not only looked into 4-qubit systems like the \(\text{H}_2\)  molecule, but also larger systems like the \(\text{LiH}\)  and \(\text{H}_2\text{O}\)  molecule as well as MaxCut on 7-node graphs. Our circuit depth is also often larger than the previous mentioned research. Since our operation pool consist of single-qubit gates on each qubit and CNOT gates either on neighbouring qubits or between every two qubits in the system, resulting a much larger size of operation pool compared to other research. With these two factors combined, our search space size is generally larger than other QAS research.
